LOS c, (Part 1): Calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding.
1、Use a stated rate of 9 percent compounded periodically to answer the following three questions. Select the choice that is the closest to the correct answer.
The semi-annual effective rate is:
A) 9.20%.
B) 9.00%.
C) 10.25%.
D) 9.31%.
The correct answer was A)
First, we need to calculate the periodic rate, or 0.09 / 2 = 0.045.
Then, the effective semi-annual rate = (1 + 0.045)2 - 1 = 0.09203, or 9.20%.
2、The quarterly effective rate is:
A) 9.31%.
B) 9.00%.
C) 9.20%.
D) 9.40%.
The correct answer was A)
First, we need to calculate the periodic rate, or 0.09 / 4 = 0.0225.
Then, the effective annual rate = (1 + 0.0225)4 - 1 = 0.09308, or 9.31%.
3、The continuously compounded rate is:
A) 9.20%.
B) 9.45%.
C) 9.42%.
D) 9.67%.
The correct answer was C)
The continuously compounded rate = er - 1 = e.09 - 1 = 0.09417, or 9.42%.
Calculator Keystrokes for et: Using the TI BA, enter [0.09] [2nd] [ex] (this is the key with LN on the face of the button). On the HP, enter [0.09] [g] [ex] (this key is located in blue on the key with 1/x in white print).
4、What is the effective annual rate if the stated rate is 12 percent compounded quarterly?
A) 12.00%.
B) 12.55%.
C) 3.00%.
D) 57.35%.
The correct answer was B)
EAR = (1 + 0.12/4)4 – 1 = 12.55%
5、A major brokerage house is currently selling an investment product that offers an 8 percent rate of return, compounded monthly. Based on this information, it follows that this investment has:
A) a stated rate of 0.830%.
B) an effective annual rate of 8.00%.
C) a periodic interest rate of 0.667%.
D) a nominal effective rate of 6.67%.
The correct answer was
Periodic rate = 8.0/12=0.667. Stated rate is 8.0% and effective rate is 8.30%.
发表于 2008-4-2 11:52
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